Consider the multiple linear regression model
Chapter 12, Problem 124MEE(choose chapter or problem)
Consider the multiple linear regression model \(\mathbf{y}=\mathbf{X} \boldsymbol{\beta}+\boldsymbol{\epsilon}\). If \(\boldsymbol{\beta}\) denotes the least squares estimator of \(\boldsymbol{\beta}\), show that \(\hat{\beta}=\beta+\mathbf{R} \epsilon\), where \(\mathbf{R}=\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \mathbf{X}^{\prime}\).
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